Boundary characteristic orthogonal polynomials method in the vibration analysis of multi-span plates acting upon a moving mass

The Boundary Characteristic Orthogonal Polynomials (BCOP) method is used in this study in order to analyze multi-span plates traversed by a moving inertia load traveling on an arbitrary path with constant velocity. The plate is assumed to be free from any support at the longitudinal edges and the spans are made by simply supported constraints at width, i.e. SFSF. The plate's mode shapes are generated by the BCOP method while the boundary condition is satisfied over all computational modes. A free vibration analysis is done in order to find natural frequency. The governing differential equations of motion are derived by Hamilton's principle and the solution in the time domain is found by using the Matrix Exponential method after modeling the problem in state space. All of the convective inertia terms are included in the acceleration derivatives and the responses are presented both for the load moving on the plate's surface ignoring/including the mass inertia effect. A comprehensive parametric study on the plate's mid-spans is carried out for the single, two- and three-span plates, investigating Dynamic Amplification Factor (DAF) versus non-dimensional velocity (V). The effect of mass and aspect ratio along with the location of reference point of calculation on the dynamic behavior of a multi-span plate is investigated and many graphs are generated as spectra. One can easily find the critical velocity as well as the peak deflection for each case study by introducing a corrective factor. The solution under moving mass excitation is obtained by the factor if the same response for moving load is known.